Former Vice President Mike Pence appeared on Thursday before the grand jury hearing evidence about former President Donald J. Trump’s efforts to cling to power after he lost the 2020 election, a person briefed on the matter said, testifying in a criminal inquiry that could shape the legal and political fate of his one-time boss and possible 2024 rival.

Mr. Pence spent more than five hours behind closed doors at the Federal District Court in Washington in an appearance that came after he was subpoenaed to testify before the grand jury earlier this year.

As the target of an intense pressure campaign in the final days of 2020 and early 2021 by Mr. Trump to convince him to play a critical role in blocking or delaying congressional certification of Joseph R. Biden Jr.’s victory, Mr. Pence is considered a key witness in the investigation.

Mr. Pence, who is expected to decide soon about whether to challenge Mr. Trump for the 2024 Republican presidential nomination, rebuffed Mr. Trump’s demands that he use his role as president of the Senate in the certification of the Electoral College results to derail the final step in affirming Mr. Biden’s victory.

Mr. Pence’s advisers had discussions with Justice Department officials last year about providing testimony in their criminal investigation into whether Mr. Trump and a number of his allies broke federal law in trying to keep Mr. Trump in power. But the talks broke down, leading prosecutors to seek a subpoena for Mr. Pence’s testimony.

Both Mr. Pence and Mr. Trump tried to fight the subpoena, with the former vice president claiming it violated the “speech or debate” clause of the Constitution given his role overseeing the election results certification on Jan. 6, 2021, and Mr. Trump claiming their discussions were covered by executive privilege.

Mr. Trump’s efforts to prevent testimony based on executive privilege claims were rebuffed by the courts. Mr. Pence partially won in his effort to forestall or limit his testimony; the chief judge overseeing the grand jury ruled that he would not have to discuss matters connected to his role as president of the Senate on Jan. 6, but that he would have to testify to any potential criminality by Mr. Trump.

A federal appeals court on Wednesday night rejected an emergency attempt by Mr. Trump to stop Mr. Pence’s testimony, allowing the testimony to go forward on Thursday.

Mr. Trump’s effort to hold onto the presidency after his defeat at the polls — and how it led to the assault on the Capitol — is the focus of one of the two federal criminal investigations being overseen by Jack Smith, a special counsel appointed by Attorney General Merrick B. Garland. Mr. Smith is also managing the parallel investigation into Mr. Trump’s handling of classified documents after leaving the White House.

Mr. Smith has gathered evidence about a wide range of activities by Mr. Trump and his allies following Election Day in 2020. They include a plan to assemble slates of alternate electors from a number of swing states who could be put forward by Mr. Trump as he disputed the Electoral College results. They also encompass an examination of whether Mr. Trump defrauded donors by soliciting contributions to fight election fraud despite having been repeatedly told that there was no evidence that the election had been stolen from him.

A district attorney in Fulton County, Ga., Fani T. Willis, has also been gathering evidence about whether Mr. Trump engaged in a conspiracy to overturn the election results in that state, and has signaled that she will announce any indictments this summer.

Mr. Pence’s unwillingness to go along with Mr. Trump’s plan to block or delay certification of the electoral outcome, infuriated Mr. Trump, who assailed his vice president privately and publicly on Jan. 6.

Mr. Pence subsequently became a target of the pro-Trump mob that swamped the Capitol building that day, with some chanting “Hang Mike Pence!” as they moved through the complex. Someone brought a fake gallows that stood outside the building.

It is not clear what testimony Mr. Pence provided on Thursday. But prosecutors were surely interested in Mr. Pence’s accounts of his interactions with Mr. Trump and Trump advisers including John Eastman, a lawyer who promoted the idea that they could use the congressional certification process on Jan. 6 to give Mr. Trump a chance to remain in office.

That plan relied on Mr. Pence using his role as president of the Senate to hold up the process. But Mr. Pence’s top lawyer and outside advisers concluded that the vice president did not have the legal authority to do so.

Mr. Pence described some of his conversations with Mr. Trump in his memoir, “So Help Me God.”

Mr. Pence described in the book how Mr. Trump worked with Mr. Eastman to pressure him into doing something that the vice president was clear that he could not and would not do. He wrote that on the morning of Jan. 6, Mr. Trump used a phone to try to bludgeon him again.

“You’ll go down as a wimp,” the president told the vice president. “If you do that, I made a big mistake five years ago!”

Some of Mr. Pence’s aides have already appeared before the grand jury, in addition to providing extensive testimony last year to the House select committee investigating the Jan. 6 riot and what led to it.